This is dividing polynomial by monomials

Question

This is dividing polynomial by monomials

How do yu solve these?

1. 5mn divided by 5m^3n - 10m^2n^2

2. -10a^6 divided by -30a^9 + 20a^7

3. -2a divided by 8a^3 - 4a^2b + 6ab^2

Answer 1

Just divide each term

Also, you have the order reversed.

5m^3n - 10m^2n^2 divided by 5mn is
m^2 - 2mn

#2: 3a^3 - 2a

#3: -4a^2 + 2ab - 3b^2

Review your rules for adding/subtracting exponents

Answer 2

To divide a polynomial by a monomial, you can follow these steps:

Step 1: Simplify the expressions by canceling out common factors, if possible.
Step 2: Divide each term of the polynomial by the monomial.

Let's apply these steps to the given problems:

1. 5mn divided by 5m^3n - 10m^2n^2

First, let's simplify the polynomials:
5mn / 5m^3n - 10m^2n^2

Notice that 5 can be cancelled out in the numerator and denominator. Also, we can simplify the exponents. After simplifying, the expression becomes:

mn / m^3n - 2m^2n^2

Now divide each term by the monomial:
(mn / m^3n) - (2m^2n^2 / m^3n)

When dividing variables with the same base, subtract the exponent of the denominator from the exponent of the numerator. The expression simplifies to:

1/m^2 - 2mn

2. -10a^6 divided by -30a^9 + 20a^7

First, let's simplify the expression:
-10a^6 / -30a^9 + 20a^7

Again, we can simplify the expression by canceling out common factors:
-10a^6 / (-30a^9 + 20a^7)

Canceling out 10 from both the numerator and denominator:
-a^6 / (-3a^9 + 2a^7)

Now divide each term by the monomial:
(-a^6 / -3a^9) + (a^6 / 2a^7)

When dividing variables with the same base, subtract the exponent of the denominator from the exponent of the numerator. The expression simplifies to:

1/3a^3 + (1/2a)

3. -2a divided by 8a^3 - 4a^2b + 6ab^2

First, let's simplify the expression:
-2a / 8a^3 - 4a^2b + 6ab^2

Now divide each term by the monomial:
(-2a / 8a^3) - (-2a / 4a^2b) + (-2a / 6ab^2)

Divide the variables by subtracting the exponents:
-1/4a^2 - (-1/2b) - (1/3b^2)

And there you have it! The expression is simplified. Remember to check if there are any common factors that can be canceled out to further simplify the expression.